Problem: Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input


4
6 3 9 12


Output


1
2

Input


2
1 2


Output


0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.

Solution (in JAVA):

Solution:
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class C {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int t = 1;

        for (int i = 0; i < t; i++) {
            long start = System.currentTimeMillis();
            solve(sc, pw);
//            System.out.println(System.currentTimeMillis() - start);
        }

        pw.close();
    }
    static void solve(Scanner in, PrintWriter out){
        int n = in.nextInt();
        int[] arr = new int[n];
        int sum = 0;
        for (int i = 0; i < n; i++) {
            arr[i] = in.nextInt();
            sum += arr[i];
        }
        if (sum % 2 != 0){
            System.out.println(0);
            return;
        }
        Map<Integer, Boolean>[] mps = new HashMap[n + 1];
        for (int i = 0; i < n + 1; i++) {
            mps[i] = new HashMap<>();
        }
        boolean get = dfs(0, mps, arr, 0);

        if (!get){
            System.out.println(0);
            return;
        }
        int[][] ak = new int[n][];
        while (true){
            for (int i = 0; i < n; i++) {
                if (arr[i] % 2 == 1){
                    out.println(1);
                    out.println((i + 1));
                    return;
                }
                arr[i] /= 2;
            }
        }
    }

    static boolean dfs(int idx,   Map<Integer, Boolean>[] mp, int[] arr, int val){
        if (idx == arr.length){
            if (val == 0){
                return true;
            }
            return false;
        }
        if  (mp[idx].containsKey(val)){
            return mp[idx].get(val);
        }

        if (dfs(idx + 1, mp, arr, val - arr[idx]) ||  dfs(idx + 1, mp, arr, val + arr[idx])){
            mp[idx].put(val, true);
            return true;
        }
        mp[idx].put(val, false);
        return false;
    }
    static boolean isPrime(long n)
    {
        // Corner cases
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;

        // This is checked so that we can skip
        // middle five numbers in below loop
        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;

        return true;
    }

    static long gcd(long a, long b)
    {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    // method to return LCM of two numbers
    static long lcm(long a, long b)
    {
        return (a / gcd(a, b)) * b;
    }

    public static int[] sieveEratosthenes(int n) {
        if (n <= 32) {
            int[] primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
            for (int i = 0; i < primes.length; i++) {
                if (n < primes[i]) {
                    return Arrays.copyOf(primes, i);
                }
            }
            return primes;
        }

        int u = n + 32;
        double lu = Math.log(u);
        int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
        ret[0] = 2;
        int pos = 1;

        int[] isnp = new int[(n + 1) / 32 / 2 + 1];
        int sup = (n + 1) / 32 / 2 + 1;

        int[] tprimes = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
        for (int tp : tprimes) {
            ret[pos++] = tp;
            int[] ptn = new int[tp];
            for (int i = (tp - 3) / 2; i < tp << 5; i += tp) ptn[i >> 5] |= 1 << (i & 31);
            for (int j = 0; j < sup; j += tp) {
                for (int i = 0; i < tp && i + j < sup; i++) {
                    isnp[j + i] |= ptn[i];
                }
            }
        }

        // 3,5,7
        // 2x+3=n
        int[] magic = {0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14};
        int h = n / 2;
        for (int i = 0; i < sup; i++) {
            for (int j = ~isnp[i]; j != 0; j &= j - 1) {
                int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
                int p = 2 * pp + 3;
                if (p > n) break;
                ret[pos++] = p;
                if ((long) p * p > n) continue;
                for (int q = (p * p - 3) / 2; q <= h; q += p) isnp[q >> 5] |= 1 << q;
            }
        }

        return Arrays.copyOf(ret, pos);
    }

    //    reverse division for 2
    public static long[] rdiv2(int n, int mod){
        long[] arr = new long[n + 5];
        arr[0] = 1;
        long rev2 = (mod + 1) / 2;
        for (int i = 1; i < n; i++) {
            arr[i] = arr[i - 1] * rev2 % mod;
        }
        return arr;
    }
}